/**
* Computes the householder vector used in QR decomposition.
*
* u = x / max(x)
* u(0) = u(0) + |u|
* u = u / u(0)
*
* @param x Input vector. Unmodified.
* @return The found householder reflector vector
*/
public static CMatrixRMaj householderVector(CMatrixRMaj x)
{
CMatrixRMaj u = (CMatrixRMaj)x.copy();
float max = CommonOps_CDRM.elementMaxAbs(u);
CommonOps_CDRM.elementDivide(u, max, 0, u);
float nx = NormOps_CDRM.normF(u);
Complex_F32 c = new Complex_F32();
u.get(0, 0, c);
float realTau, imagTau;
if (c.getMagnitude() == 0)
{
realTau = nx;
imagTau = 0;
}
else
{
realTau = c.real / c.getMagnitude() * nx;
imagTau = c.imaginary / c.getMagnitude() * nx;
}
u.set(0, 0, c.real + realTau, c.imaginary + imagTau);
CommonOps_CDRM.elementDivide(u, u.getReal(0, 0), u.getImag(0, 0), u);
return(u);
}
/**
* <p>
* Computes the Frobenius matrix norm:<br>
* <br>
* normF = Sqrt{ ∑<sub>i=1:m</sub> ∑<sub>j=1:n</sub> { a<sub>ij</sub><sup>2</sup>} }
* </p>
* <p>
* This is equivalent to the element wise p=2 norm.
* </p>
*
* @param a The matrix whose norm is computed. Not modified.
* @return The norm's value.
*/
public static float normF(CMatrixRMaj a)
{
float total = 0;
float scale = CommonOps_CDRM.elementMaxAbs(a);
if (scale == 0.0f)
{
return(0.0f);
}
int size = a.getDataLength();
for (int i = 0; i < size; i += 2)
{
float real = a.data[i] / scale;
float imag = a.data[i + 1] / scale;
total += real * real + imag * imag;
}
return(scale * (float)Math.Sqrt(total));
}